Final answer:
The frictional force required to hold the stopper in the vertical cylindrical tube is approximately 3.07 N.
Step-by-step explanation:
To calculate the frictional force required to hold the stopper in the vertical cylindrical tube, we need to consider the pressure difference between the top and bottom of the water column.
The pressure difference is given by the equation:
ΔP = ρgh
where ρ is the density of water, g is the acceleration due to gravity, and h is the height of the water column.
Since the tube is filled to a height of 1 m, we can substitute the values into the equation:
ΔP = (1000 kg/m³)(9.8 m/s²)(1 m) = 9800 N/m²
The frictional force required to hold the stopper in the tube equals the pressure difference multiplied by the cross-sectional area of the tube:
F = ΔP × A
Since the radius of the tube is 1 cm, we can calculate the cross-sectional area:
A = πr² = π(0.01 m)² = 0.000314 m²
Substituting the values:
F = 9800 N/m² × 0.000314 m² = 3.07 N
Therefore, the frictional force required to hold the stopper in the tube is approximately 3.07 N.